static char help[] = "Newton's method for a two-variable system, sequential.\n\n"; /*T Concepts: SNES^basic example T*/ /* Include "petscsnes.h" so that we can use SNES solvers. Note that this file automatically includes: petscsys.h - base PETSc routines petscvec.h - vectors petscmat.h - matrices petscis.h - index sets petscksp.h - Krylov subspace methods petscviewer.h - viewers petscpc.h - preconditioners petscksp.h - linear solvers */ /*F This examples solves either $$F\genfrac{(}{)}{0pt}{}{x_0}{x_1} = \genfrac{(}{)}{0pt}{}{x^2_0 + x_0 x_1 - 3}{x_0 x_1 + x^2_1 - 6}$$ or if the {\tt -hard} options is given $$F\genfrac{(}{)}{0pt}{}{x_0}{x_1} = \genfrac{(}{)}{0pt}{}{\sin(3 x_0) + x_0}{x_1}$$ F*/ #include /* User-defined routines */ extern PetscErrorCode FormJacobian1(SNES,Vec,Mat,Mat,void*); extern PetscErrorCode FormFunction1(SNES,Vec,Vec,void*); extern PetscErrorCode FormJacobian2(SNES,Vec,Mat,Mat,void*); extern PetscErrorCode FormFunction2(SNES,Vec,Vec,void*); int main(int argc,char **argv) { SNES snes; /* nonlinear solver context */ KSP ksp; /* linear solver context */ PC pc; /* preconditioner context */ Vec x,r; /* solution, residual vectors */ Mat J; /* Jacobian matrix */ PetscErrorCode ierr; PetscMPIInt size; PetscScalar pfive = .5,*xx; PetscBool flg; ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr); if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Example is only for sequential runs"); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create nonlinear solver context - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = SNESCreate(PETSC_COMM_WORLD,&snes);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create matrix and vector data structures; set corresponding routines - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* Create vectors for solution and nonlinear function */ ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr); ierr = VecSetSizes(x,PETSC_DECIDE,2);CHKERRQ(ierr); ierr = VecSetFromOptions(x);CHKERRQ(ierr); ierr = VecDuplicate(x,&r);CHKERRQ(ierr); /* Create Jacobian matrix data structure */ ierr = MatCreate(PETSC_COMM_WORLD,&J);CHKERRQ(ierr); ierr = MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,2,2);CHKERRQ(ierr); ierr = MatSetFromOptions(J);CHKERRQ(ierr); ierr = MatSetUp(J);CHKERRQ(ierr); ierr = PetscOptionsHasName(NULL,NULL,"-hard",&flg);CHKERRQ(ierr); if (!flg) { /* Set function evaluation routine and vector. */ ierr = SNESSetFunction(snes,r,FormFunction1,NULL);CHKERRQ(ierr); /* Set Jacobian matrix data structure and Jacobian evaluation routine */ ierr = SNESSetJacobian(snes,J,J,FormJacobian1,NULL);CHKERRQ(ierr); } else { ierr = SNESSetFunction(snes,r,FormFunction2,NULL);CHKERRQ(ierr); ierr = SNESSetJacobian(snes,J,J,FormJacobian2,NULL);CHKERRQ(ierr); } /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Customize nonlinear solver; set runtime options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* Set linear solver defaults for this problem. By extracting the KSP and PC contexts from the SNES context, we can then directly call any KSP and PC routines to set various options. */ ierr = SNESGetKSP(snes,&ksp);CHKERRQ(ierr); ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr); ierr = PCSetType(pc,PCNONE);CHKERRQ(ierr); ierr = KSPSetTolerances(ksp,1.e-4,PETSC_DEFAULT,PETSC_DEFAULT,20);CHKERRQ(ierr); /* Set SNES/KSP/KSP/PC runtime options, e.g., -snes_view -snes_monitor -ksp_type -pc_type These options will override those specified above as long as SNESSetFromOptions() is called _after_ any other customization routines. */ ierr = SNESSetFromOptions(snes);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Evaluate initial guess; then solve nonlinear system - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ if (!flg) { ierr = VecSet(x,pfive);CHKERRQ(ierr); } else { ierr = VecGetArray(x,&xx);CHKERRQ(ierr); xx[0] = 2.0; xx[1] = 3.0; ierr = VecRestoreArray(x,&xx);CHKERRQ(ierr); } /* Note: The user should initialize the vector, x, with the initial guess for the nonlinear solver prior to calling SNESSolve(). In particular, to employ an initial guess of zero, the user should explicitly set this vector to zero by calling VecSet(). */ ierr = SNESSolve(snes,NULL,x);CHKERRQ(ierr); if (flg) { Vec f; ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); ierr = SNESGetFunction(snes,&f,0,0);CHKERRQ(ierr); ierr = VecView(r,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); } /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Free work space. All PETSc objects should be destroyed when they are no longer needed. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = VecDestroy(&x);CHKERRQ(ierr); ierr = VecDestroy(&r);CHKERRQ(ierr); ierr = MatDestroy(&J);CHKERRQ(ierr); ierr = SNESDestroy(&snes);CHKERRQ(ierr); ierr = PetscFinalize(); return ierr; } /* ------------------------------------------------------------------- */ /* FormFunction1 - Evaluates nonlinear function, F(x). Input Parameters: . snes - the SNES context . x - input vector . ctx - optional user-defined context Output Parameter: . f - function vector */ PetscErrorCode FormFunction1(SNES snes,Vec x,Vec f,void *ctx) { PetscErrorCode ierr; const PetscScalar *xx; PetscScalar *ff; /* Get pointers to vector data. - For default PETSc vectors, VecGetArray() returns a pointer to the data array. Otherwise, the routine is implementation dependent. - You MUST call VecRestoreArray() when you no longer need access to the array. */ ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr); ierr = VecGetArray(f,&ff);CHKERRQ(ierr); /* Compute function */ ff[0] = xx[0]*xx[0] + xx[0]*xx[1] - 3.0; ff[1] = xx[0]*xx[1] + xx[1]*xx[1] - 6.0; /* Restore vectors */ ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr); ierr = VecRestoreArray(f,&ff);CHKERRQ(ierr); return 0; } /* ------------------------------------------------------------------- */ /* FormJacobian1 - Evaluates Jacobian matrix. Input Parameters: . snes - the SNES context . x - input vector . dummy - optional user-defined context (not used here) Output Parameters: . jac - Jacobian matrix . B - optionally different preconditioning matrix . flag - flag indicating matrix structure */ PetscErrorCode FormJacobian1(SNES snes,Vec x,Mat jac,Mat B,void *dummy) { const PetscScalar *xx; PetscScalar A[4]; PetscErrorCode ierr; PetscInt idx[2] = {0,1}; /* Get pointer to vector data */ ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr); /* Compute Jacobian entries and insert into matrix. - Since this is such a small problem, we set all entries for the matrix at once. */ A[0] = 2.0*xx[0] + xx[1]; A[1] = xx[0]; A[2] = xx[1]; A[3] = xx[0] + 2.0*xx[1]; ierr = MatSetValues(B,2,idx,2,idx,A,INSERT_VALUES);CHKERRQ(ierr); /* Restore vector */ ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr); /* Assemble matrix */ ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); if (jac != B) { ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); } return 0; } /* ------------------------------------------------------------------- */ PetscErrorCode FormFunction2(SNES snes,Vec x,Vec f,void *dummy) { PetscErrorCode ierr; const PetscScalar *xx; PetscScalar *ff; /* Get pointers to vector data. - For default PETSc vectors, VecGetArray() returns a pointer to the data array. Otherwise, the routine is implementation dependent. - You MUST call VecRestoreArray() when you no longer need access to the array. */ ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr); ierr = VecGetArray(f,&ff);CHKERRQ(ierr); /* Compute function */ ff[0] = PetscSinScalar(3.0*xx[0]) + xx[0]; ff[1] = xx[1]; /* Restore vectors */ ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr); ierr = VecRestoreArray(f,&ff);CHKERRQ(ierr); return 0; } /* ------------------------------------------------------------------- */ PetscErrorCode FormJacobian2(SNES snes,Vec x,Mat jac,Mat B,void *dummy) { const PetscScalar *xx; PetscScalar A[4]; PetscErrorCode ierr; PetscInt idx[2] = {0,1}; /* Get pointer to vector data */ ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr); /* Compute Jacobian entries and insert into matrix. - Since this is such a small problem, we set all entries for the matrix at once. */ A[0] = 3.0*PetscCosScalar(3.0*xx[0]) + 1.0; A[1] = 0.0; A[2] = 0.0; A[3] = 1.0; ierr = MatSetValues(B,2,idx,2,idx,A,INSERT_VALUES);CHKERRQ(ierr); /* Restore vector */ ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr); /* Assemble matrix */ ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); if (jac != B) { ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); } return 0; } /*TEST test: args: -ksp_gmres_cgs_refinement_type refine_always -snes_monitor_short requires: !single test: suffix: 2 requires: !single args: -snes_monitor_short output_file: output/ex1_1.out test: suffix: 3 args: -ksp_view_solution ascii:ex1_2_sol.tmp:ascii_matlab -snes_monitor_short requires: !single output_file: output/ex1_1.out test: suffix: 4 args: -ksp_view_solution ascii:ex1_2_sol.tmp::append -snes_monitor_short requires: !single output_file: output/ex1_1.out test: suffix: 5 args: -ksp_view_solution ascii:ex1_2_sol.tmp:ascii_matlab:append -snes_monitor_short requires: !single output_file: output/ex1_1.out test: suffix: 6 args: -ksp_view_solution ascii:ex1_2_sol.tmp:default:append -snes_monitor_short requires: !single output_file: output/ex1_1.out test: suffix: X args: -ksp_monitor_short -ksp_type gmres -ksp_gmres_krylov_monitor -snes_monitor_short -snes_rtol 1.e-4 requires: !single x TEST*/